New mathematical programming approaches for assemble-to-order system optimization

装配订单（ATO）系统代表了当代经济中一类重要的制造系统，特别是在高科技领域。ATO系统运行优化涉及到复杂的随机优化问题。由于这一困难，行业实践与快速增长的学术文献之间存在很大差距。在本研究中，我们开发了一种称为“多匹配”的概念创新来表征ATO系统。从这一创新开始，我们提出了新的随机规划模型，可以在ATO系统中纳入关键的随机元素，同时拥抱数学规划的计算能力。我们的目标是准确地解决中小型实例，为现实生活中的大型系统提供具有性能保证的良好解决方案。所提出的方法在学术界和工业界都有几个重要的含义。首先，随机规划模型为ATO系统注入了新的见解，可以为行业实践和文献中已有的启发式提供统一的基准。其次，概念创新和相应的数学程序可以应用于非常普遍的库存系统。它们可以用来研究客户差异化服务措施、供应风险、随机交货时间和产量不确定性的影响。它们也可以扩展到多产品和多级库存系统。第三，本研究提供了最先进的随机规划技术的重要应用，给数学规划的建模和计算带来了新的挑战和机遇。拟议的研究计划将培养具有库存理论、随机规划/数学规划和ERP软件专业知识的博士，以及具有现实生活中ATO系统和ERP软件专业知识的硕士。

Assemble-To-Order (ATO) systems represent a large class of important manufacturing systems in the contemporary economy, especially in the high-tech sector. The optimization of ATO system operations involves difficult stochastic optimization problems. Due to this difficulty, there is a big gap between the industrial practice and the fast growing academic literature on this topic. In this research, we develop a conceptual innovation called "multi-matching" on characterizing the ATO systems. Starting from this innovation, we propose new stochastic programming models that can incorporate the critical stochastic elements in ATO systems, while embracing the computational power of mathematical programming. We aim at solving small- to medium-sized instances accurately, and providing good solutions with performance guarantee for large-scale systems in real life. The proposed approaches have several important implications in both academia and industry. Firstly, the stochastic programming models inject new insights into the ATO systems, and can provide a uniform benchmark for the practice in the industry and the existing heuristics in the literature. Secondly, the conceptual innovation and the corresponding mathematical programs can be applied to very general inventory systems. They can be used to study the impact of customer-differentiated service measures, supply risks, stochastic lead times and yield uncertainty. They can also be extended to multi-product and multi-echelon inventory systems. Thirdly, this research provides an important application of the state-of-the-art stochastic programming techniques, and brings new challenges and opportunities to both the modeling and computation of mathematical programming. The proposed research program will train Ph.D.'s with the expertise in inventory theory, stochastic programming / mathematical programming, and ERP software, and M.Sc.'s with the expertise in real life ATO systems, and ERP software.